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Enforcing complex (e.g., nonconvex) operational constraints is a critical challenge in real-world learning and control systems. However, existing methods struggle to efficiently enforce general classes of constraints. To address this, we…

Reliably knowing when a language model is correct is almost as important as being correct. We introduce prover-verifier deliberation (PVD), an inference-time protocol grounded in interactive proof theory, as a mechanism for selective…

We proposed a framework for solving inverse problems in differential equations based on neural networks and automatic differentiation. Neural networks are used to approximate hidden fields. We analyze the source of errors in the framework…

We present a method for synthesizing recursive functions that provably satisfy a given specification in the form of a polymorphic refinement type. We observe that such specifications are particularly suitable for program synthesis for two…

Formal verification via theorem proving enables the expressive specification and rigorous proof of software correctness, but it is difficult to scale due to the significant manual effort and expertise required. While Large Language Models…

Legacy systems concentrate business rules, architectural decisions, and operational exceptions that often remain implicit in code, data, configuration, and maintenance practices. At the same time, language-model-based coding agents depend…

This paper introduces the continuous tensor abstraction, allowing indices to take real-number values (for example, A[3.14]). It also presents continuous tensor algebra expressions, such as C(x,y) = A(x,y) * B(x,y), where indices are defined…

Current deep learning-based solutions for image analysis tasks are commonly incapable of handling problems to which multiple different plausible solutions exist. In response, posterior-based methods such as conditional Diffusion Models and…

Code language models are increasingly adopted for both understanding and generative tasks. Despite their success, these models frequently produce overconfident incorrect predictions and underconfident correct predictions, undermining their…

Catching and attributing code change-induced performance regressions in production is hard; predicting them beforehand, even harder. A primer on automatically learning to predict performance regressions in software, this article gives an…

For large software applications, running the whole test suite after each code change is time- and resource-intensive. Regression test selection techniques aim at reducing test execution time by selecting only the tests that are affected by…

High-performance tensor programs are crucial to guarantee efficient execution of deep neural networks. However, obtaining performant tensor programs for different operators on various hardware platforms is notoriously challenging.…

Some total languages, like Agda and Coq, allow the use of guarded corecursion to construct infinite values and proofs. Guarded corecursion is a form of recursion in which arbitrary recursive calls are allowed, as long as they are guarded by…

We investigate proving properties of Curry programs using Agda. First, we address the functional correctness of Curry functions that, apart from some syntactic and semantic differences, are in the intersection of the two languages. Second,…

Despite a lack of theoretical understanding, deep neural networks have achieved unparalleled performance in a wide range of applications. On the other hand, shallow representation learning with component analysis is associated with rich…

Safe deployment of AI models requires proactive detection of failures to prevent costly errors. To this end, we study the important problem of detecting failures in deep regression models. Existing approaches rely on epistemic uncertainty…

Programs with constraints are hard to debug. In this paper, we describe a general architecture to help develop new debugging tools for constraint programming. The possible tools are fed by a single general-purpose tracer. A tracer-driver is…

We introduce a framework, which we denote as the augmented estimate sequence, for deriving fast algorithms with provable convergence guarantees. We use this framework to construct a new first-order scheme, the Accelerated Composite Gradient…

Many applications of large language models (LLMs) require deductive reasoning, yet models frequently produce incorrect or redundant inference steps. We frame natural language inference as a search problem where the final answer is the valid…

Automatic spelling and grammatical correction systems are one of the most widely used tools within natural language applications. In this thesis, we assume the task of error correction as a type of monolingual machine translation where the…